Sentence Examples


  • Gockel (37) says that the results he obtained without the cover when divided by 3 are fairly comparable with those obtained under the usual conditions; but the appropriate divisor must vary to some extent with the climatic conditions.
  • It will be noticed that the rods only give the multiples of the number which is to be multiplied, or of the divisor when they are used for division, and it is evident that they would be of little use to any one who knew the multiplication table as far as 9 X9.
  • In multiplications or divisions of any length it is generally convenient to begin by forming a table of the first nine multiples of the multiplicand or divisor, and Napier's bones at best merely provide such a table, and in an incomplete form, for the additions of the two figures in the same parallelogram have to be performed each time the rods are used.
  • (ii.) The elements of the theory of numbers belong to arithmetic. In particular, the theorem that if n is a factor of a and of b it is also a factor of pa= qb, where p and q are any integers, is important in reference to the determination of greatest common divisor and to the elementary treatment of continued fractions.
  • Moreover, if the last divisor is uL, then it follows from the theory of numbers (� 26 (ii.)) that (a) u is a factor of p and of q, and (b) any number which is a factor of p and q is also a factor of u.

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